Why We Don't Diffract Around Trees: Quantum Effects In The Macroscopic World.

A common misapprehension of quantum physics, especially by woo-merchants and pseudoscience practitioners is the implication that quantum effects should, or are seen in the macroscopic world around us. As an example, Teresa Tsalaky here explains to us that various quantum effects are the reasons various alternative medicines work beyond placebo, of course, she never explains how they explain these things.

"If you want to understand why ancient healing methods work, look to humankind’s most modern science: quantum physics. Wave-particle duality, the properties of electromagnetic fields, the holographic effect, the impact of the observer—these discoveries can help explain so much. They unlock the secrets of how homeopathy cures, why the holistic approach is so effective, how Reiki and Qigong can heal tissues, what makes iridology an effective diagnostic tool, and why placebos work about thirty percent of the time." (0)

But she's right about one thing, all matter can be described as a wave right? This is as good a place as any to start explaining why the weird and wonderful effects of quantum physics stay restricted to the microscopic realm and do not leak into our macroscopic lives.

Take this scenario.

It's your first day on a new job, eager to impress you leave for work early. Unfortunately, your car won't start, you'll have to travel by bus. You arrive at the bus stop just as your bus is pulling away, You run for the bus, but unfortunately, you run smack bang into a tree. This results in you arriving late. 

Later on during your first day, the boss calls to her office. She wants to know why you were late and why your face is hideously disfigured. You explain about running into the tree.

Your boss looks at you sternly, "You're lying." she says "Don't you know quantum physics? All matter displays wavelike behaviour. You would have just diffracted around that tree. Clear your desk." 

So why don't we demonstrate wave-like behaviour? Why didn't you diffract around that tree? Why throw thrown balls diffract around baseball bats and tennis rackets?

To answer this we need to consider the De Broglie wave and one of the most important elements of quantum physics: Planck's constant.

It was Louis De Broglie (1892-1987) who first suggested that matter, like photons, should demonstrate particle and wave-like behaviour. Electrons, De Broglie suggested should diffract around objects just as light waves and water waves do (1). This wave like nature of matter was first demonstrated experimentally with a stream of electrons by Thompson in the UK and by Davidson-Germer in the US (2) separately and roughly simultaneously. The evidence of the wave-like behaviour of electrons is given by the appearance of an interference pattern at the electron detector screen. Where peaks intersect there are bright peaks or constructive interference, where troughs of the waves intersect there are dark strips where no electrons are detected or destructive interference.  An example of this is seen below, but it's important to note this isn't the Davisson-Germer set up.

The parameters of this matter-wave, also known as the De Brogle wave (the name we'll continue to use) or the probability wave, are given by the relationship:

Where h is Planck's constant and p is the magnitude of the particle's momentum which is in turn, for a particle with mass given by: 

The key to wave like behaviour at the quantum scale lies in the size of Planck's constant in comparison to the particle's momentum. Planck's constant has a value of

which is a decimal point followed by 33 zeroes. As you can see it's an extremely small constant and is found through out quantum physics in this or another form. Diffraction only occurs when the size of the wavelength of the travelling wave or particle is comparable in size to the gap through which it passes or the object around which it's diffracting. Think about FM radio waves which are electromagnetic radiation with a wavelength of roughly 1km, these will diffract around large objects like buildings. Whereas we know from the fact we can't see what is directly behind large buildings that visible light with a wavelength of between 400 -700 nm cannot diffract around these objects.

Now for an electron with a mass of 10^-30 kg travelling at roughly six million meters per second, the De Broglie wavelength is:

Which is roughly about a tenth of a nanometer. This explains why electrons diffract from a sheet of nickel as seen in the Davisson-Germer experiment, the De Broglie wavelength is roughly half the distance between two nickel atoms.





Let's compare this to the De Broglie wavelength of the average human being running for a bus. Let's take the average global body mass of 62 kg and let's say our running speed is 3 m/s when we hit the tree.Which gives us:

As you can see the De Broglie wave-length for a macroscopic object is incredibly small in comparison to that of an atom. To demonstrate this isn't just for a human being, let's look at the reason we don't see a tennis ball diffract around a  tennis racket at Wimbledon. Let's take the mass of the ball to be 0.06 kg and the magnitude of its velocity to be 60 m/s.

So we wouldn't expect a diffraction from a meter or so wide tree simply because of the massive difference in size, and that massive difference in size continues through tennis balls and rackets way down to, as far as we can see thus far particles of roughly 5000 protons, neutrons and electrons (3) with the formula C284.H190.F320.N4.S12. The momentum aspect of the De Broglie equation is simply too large, and Planck's constant too small, for even small slow moving objects for the wave-like behaviour to be demonstrated at macroscopic levels.

So we can see that the tiny value of Planck's constant (h) is the reason we don't see particle-wave duality in the macroscopic world, but it turns out this is the mitigating factor in why we don't see other quantum effects such as the Heisenberg uncertainty principle in classical physics.

That's where we head next.

Sources

(0) http://pathwaystofamilywellness.org/Inspirational/traditional-healing-modern-science.html

(1) https://en.wikipedia.org/wiki/Electron_diffraction

(2) https://en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment

(3) https://medium.com/the-physics-arxiv-blog/physicists-smash-record-for-wave-particle-duality-462c39db8e7b

All equations and constants: The Quantum World: Wave Mechanics (Bolton, Lambourne, 2007), Quantum Physics: An Introduction (Manners, 2000)